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Results for “BOUNDARY-VALUE PROBLEMS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Initial-Boundary Value Problem for the Nonstationary Radiative Transfer Equation with Diffuse Reflection and Refraction Conditions

We consider the initial-boundary value problem for the nonstationary radiative transfer equation in a system of semitransparent bodies with the conditions of diffuse reflection and refraction of radiation. We establish the unique solvability of the problem with boundary and initial data in the complete scale of Lebesgue spaces. We obtain estimates for solutions.

42 ENGINEERING↗
DOE OSTI2018

Smoothness in the Dini Space of a Single Layer Potential for a Parabolic System in the Plane

We prove estimates in the Dini space for the second order spatial derivative of a vector parabolic single layer potential. We obtain estimates for higher order derivatives of solutions to initial-boundary-value problems for one-dimensional parabolic systems with Dini-continuous coefficients in a curvilinear domain with nonsmooth lateral boundary.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Universal Method of Modeling Linear Stationary Physical Fields

The aim of this paper is to develop a method, described earlier, of solving quantum-mechanical problems into a universal numerical method of modeling fields of various physical nature. This method is based on reducing the initial equation of mathematical physics describing a given physical field to a simpler inhomogeneous equation with a known fundamental solution. This equation is then transformed into an inhomogeneous integral equation with a kernel expressed in terms of the known fundamental solution. The obtained integral equation with boundary conditions is solved numerically. To confirm the efficiency of the proposed numerical method, a two-dimensional and a three-dimensional boundary value problem with known solutions have been solved. Another important illustration of the efficiency of the proposed method is the solution of quantum-mechanical problems for one-dimensional and two-dimensional quantum oscillators. It is shown that the considered method allows one to find the energy eigenvalues and the eigenfunctions with acceptable accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Solution of A. Einstein’s Problem on the Density of Matter in the Universe

On the basis of the special theory of relativity and a solution of the Schwarzschild equations of general relativity, a generalized equation of Friedmann–Einstein–de Sitter type has been obtained for the expanding Universe. As a result of our work on the boundary value problem for this equation, we have found the eigenvalue of the resulting eigenvalue problem, linking the density of the Universe in the comoving coordinates, the Hubble constant, and the gravitational constant. We have calculated a value for the density of matter in the Universe which is in agreement with the observational data. We have shown that the missing dark energy is the relativistic kinematic and potential energy of the expanding Universe.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The influence of interval arithmetic on the shape of uncertainly defined domains modelled by closed curves

The paper presents an unambiguous modelling of imprecisely defined shapes of closed curves using classical and directed interval arithmetic. The authors focus on the development of an effective strategy of modelling interval smooth closed curves (which enforce C{sup 2} continuity in points at which adjacent interval segments join) using interval cubic Bézier segments. For this purpose, algebraic relationships between Bézier and de Boor control points, formerly known for precisely defined curves, are generalized. We obtain interval control points that define interval closed curves. Additionally, the reliability of such way of modelling of closed curves is examined. We directly apply classical and directed interval arithmetic to mentioned relationships and try to solve obtained interval systems of algebraic equations. However, we obtain ambiguous solutions. Therefore, we propose our new strategy of modification of directed interval arithmetic to obtain reliable and unambiguous shapes of interval closed curves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical similarity solution for a variable coefficient K(m, n) equation

A technique for finding numerical similarity solutions to an initial boundary value problem (IBVP) for generalized K(m, n) equations is described. The equation under consideration is nonlinear and has variable coefficients. The original problem is transformed with the aid of Lie symmetries to an initial value problem (IVP) for a nonlinear third-order ordinary differential equation. The existence and uniqueness of the solution are examined, and the problem is consequently solved with the aid of a finite-difference scheme for various values of the governing parameters. In lieu of an exact symbolic solution, the scheme is validated by comparing the numerical solutions with the approximate analytic solutions obtained with the aid of the method of successive approximations in their region of validity. The accuracy, efficiency, and consistency of the scheme are demonstrated. Numerical solutions to the original initial boundary value problem are constructed for selected parameter values with the aid of the transforms. The qualitative behavior of the solutions as a function of the governing parameters is analyzed, and it is found that the examined IBVPs for generalized K(m, n) equations with variable coefficients that are functions of time, do not admit solitary wave or compacton solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An asymmetric backward problem for the inhomogeneous parabolic equation with time-dependent diffusivity

In this paper, we deal with an asymmetric case of the non-homogeneous backward parabolic problem associated with time-dependent diffusivity in polar coordinates which arises in describing the heat transfer in cylinder. In general, this problem is severely ill-posed by the Hadamard instability. To subdue the instability of this problem, we apply the modified quasi-boundary value method. According to some a priori assumptions on the exact solution, we get an explicit error estimate of Hölder type for all t∈(0,T]. In addition, a numerical experiment is given to illustrate the efficiency and flexibility of our method.

42 ENGINEERING↗
DOE OSTI2018

Reconstructing the membrane detection of a 1D electrostatic-driven MEMS device by the shooting method: convergence analysis and ghost solutions identification

In this paper, in the domain of 1D-membrane micro-electro-mechanical systems in which the electrostatic field is expressed in terms of geometric curvature of the membrane, we present a numerical approach based on shooting techniques to reconstruct the membrane profile in the device in steady-state case. In particular, starting from known results in literature about existence achieved by Schauder–Tychonoff’s fixed point approach and uniqueness, and focusing on two physical–mathematical parameters appropriately indicative of the applied voltage and electromechanical properties of the membrane, respectively, we will discuss what operation parameters (applied voltage, amplitude of electrostatic field) and for which electromechanical membrane characteristic of the device is permitted or not a convergence of the method with respect to analytical results. Finally, we will discuss in detail the detected ghost solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for the Euler equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Convergence of multipoint Pade approximants of piecewise analytic functions

The behaviour as n{yields}{infinity} of multipoint Pade approximants to a function which is (piecewise) holomorphic on a union of finitely many continua is investigated. The convergence of multipoint Pade approximants is proved for a function which extends holomorphically from these continua to a union of domains whose boundaries have a certain symmetry property. An analogue of Stahl's theorem is established for two-point Pade approximants to a pair of functions, either of which is a multivalued analytic function with finitely many branch points. Bibliography: 11 titles.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2009

Investigation of Boundary Conditions for Flexible Multibody Spacecraft Dynamics

In support of both the Space Shuttle and International Space Station programs, a set of generic multibody dynamics algorithms integrated within the Trick simulation environment have addressed the variety of on-orbit manipulator simulation requirements for engineering analysis, procedures development and crew familiarization/training at the NASA Johnson Space Center (JSC). Enhancements to these dynamics algorithms are now being driven by a new set of Constellation program requirements for flexible multibody spacecraft simulation. One particular issue that has been discussed within the NASA community is the assumption of cantilever-type flexible body boundary conditions. This assumption has been commonly utilized within manipulator multibody dynamics formulations as it simplifies the computation of relative motion for articulated flexible topologies. Moreover, its use for modeling of space-based manipulators such as the Shuttle Remote Manipulator System (SRMS) and Space Station Remote Manipulator System (SSRMS) has been extensively validated against flight data. For more general flexible spacecraft applications, however, the assumption of cantilever-type boundary conditions may not be sufficient. This paper describes the boundary condition assumptions that were used in the original formulation, demonstrates that this formulation can be augmented to accommodate systems in which the assumption of cantilever boundary conditions no longer applies, and verifies the approach through comparison with an independent model previously validated against experimental hardware test data from a spacecraft flexible dynamics emulator.

Boundary-value problems↗
NASA NTRS1990

Computing Deformations Of Rubbery Materials

Better use made of experimental data in finite-element computations. New formulation of constitutive equations of rubbery, nonlinearly elastic material enables finite-element analysis of boundary-value stress-and-strain problems involving arbitrary shapes and loads. In development of formulation, principal stretches used as arguments of strain-energy-density function.

Peng, Steven T. J.↗
NASA NTRS1990

Solving time-dependent two-dimensional eddy current problems

Transient eddy current calculations are presented for an EM wave-scattering and field-penetrating case in which a two-dimensional transverse magnetic field is incident on a good (i.e., not perfect) and infinitely long conductor. The problem thus posed is of initial boundary-value interface type, where the boundary of the conductor constitutes the interface. A potential function is used for time-domain modeling of the situation, and finite difference-time domain techniques are used to march the potential function explicitly in time. Attention is given to the case of LF radiation conditions.

Lee, Min Eig↗
NASA NTRS1989

Singular trajectories for time-optimal half-loop maneuvers of a high alpha fighter aircraft

Consideration is given to the problem of deriving a time-optimal open-loop control for the half-loop maneuver of a high-alpha aircraft, with initial conditions Mach 0.6 and 15,000 feet. Pontriagin's maximum principle is used to derive candidate optimal solutions. Using the two-point boundary-value algorithm, the flight path angle is maximized for various increasing specified final times until a final time of 13.6 sec yields a 180-deg flight-path angle. As the final time increased from 0.0 to 13.6 sec, the optimization process revealed 13 distinct switching structures of the control law, of which 11 contained singular arcs, and two had double singular arcs.

Hoffman, Eric↗
NASA NTRS1990

Spurious frequencies as a result of numerical boundary treatments

The stability theory for finite difference Initial Boundary-Value approximations to systems of hyperbolic partial differential equations states that the exclusion of eigenvalues and generalized eigenvalues is a sufficient condition for stability. The theory, however, does not discuss the nature of numerical approximations in the presence of such eigenvalues. In fact, as was shown previously, for the problem of vortex shedding by a 2-D cylinder in subsonic flow, stating boundary conditions in terms of the primitive (non-characteristic) variables may lead to such eigenvalues, causing perturbations that decay slowly in space and remain periodic time. Characteristic formulation of the boundary conditions avoided this problem. A more systematic study of the behavior of the (linearized) one-dimensional gas dynamic equations under various sets of oscillation-inducing legal boundary conditions is reported.

Abarbanel, Saul↗
DOE OSTI2019

Combination of the Laguerre Transform with the Boundary-element Method for the Solution of Integral Equations with Retarded Kernel

We apply the Laguerre transform with respect to time to a time-dependent boundary-value integral equation encountered in the solution of three-dimensional Dirichlet initial-boundary-value problems for the homogeneous wave equation with homogeneous initial conditions by using the retarded potential of single layer. The obtained system of boundary integral equations is reduced to a sequence of Fredholm integral equations of the first kind that differ solely by the recursively dependent right-hand sides. To find their numerical solution, we use the boundary-element method. We establish an asymptotic estimate of the error of numerical solution and present the results of numerical simulations aimed at finding the solutions of retarded-potential integral equations for model examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Altitude/path-angle transitions in fuel-optimal problems for transport aircraft

Altitude/path angle transitions to fuel-optimal, energy climb and descent paths are examined for subsonic transport aircraft. These transitions are termed boundary layers in singular perturbation theory, the framework used herein to simplify solutions to the state-Euler system. The energy climb and descent paths provide equilibrium or stationary points for the boundary layer system, and thus for moderate transitions, presumed valid for the class of aircraft considered, the boundary layer system may be linearized. This simplification allows derivation of an explicit solution to the two-point boundary-value, boundary layer problem and, as a consequence, yields a nearly optimal control law, in feedback form, for the transitions. Numerical simulation results using the feedback control law are presented for a Boeing 737 airframe (NASA-ATOPS Vehicle) employing twin JT8D-7-7A engines.

Gracey, C.↗
NASA NTRS1992

Computational aspects of helicopter trim analysis and damping levels from Floquet theory

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Gaonkar, Gopal H.↗